A couple of good references that came up with a quick Google search:
Grammarly Blog: Which vs. That
Writer's Digest: which vs that
In summary, which one to use depends on whether the information being added is essential to the meaning of the overall sentence or not.
In the first sentence:
The movie ___ I saw yesterday was good.
this actually may ...
Clues and prepositions
Let’s look at some examples of the use of clue/s from the [Cambridge Dictionary on-line]:
The police tried to reconstruct the crime using…clues that they had found. [No preposition]
The police found a vital clue to the girl's disappearance… [Preposition, to]
He pored over the letter searching for clues about the writer. [...
X will provide clues. [no to]
These cars belong to a category. [belong to a category]
X will provide clues to which category the cars belong.
One is hard pressed to concoct a mistake in The Economist's sentence:
Aston Martin’s IPO will provide further clues // to which category ultra-expensive carmakers really belong.
The parse is shown by the slash
Bill J wrote:
It's an error: "which category ultra-expensive carmakers really belong to" is a subordinate interrogative clause (embedded question) where the meaning is "Aston Martin’s IPO will provide further clues to the answer to the question 'Which category do ultra-expensive carmakers really belong to?'
I liked the pen ( which /that) you gave to Mke
That is the sentence you gave
It can be divided into two sentences as shown below.
I liked a pen.You gave it (the pen ) to Mike.
As Fumble Fingers rightly pointed out in his comment, the sentence reads better this way.
You gave Mike the pen (that/ which) I liked
Now this ...